To some degree, this is an unavoidable responsibility of DMing. You have to decide if the fortification wall is made of wood or stone, and whether it's smooth or rough and all of that will produce a climb DC. Some of that comes down to professional responsibility to make those decisions based on some consistent set of criteria (internally consistent worldbuilding, scaling player capability, extrapolation from some standard, there's several approaches that can work here). Beyond that, I think this can and should be mitigated in a few ways.
See below for explication, but I think the primary concern is scaling with some affordance made for consistency with worldbuilding. Given that, scaling DCs make some sense. If you want a number that fits the current context, it’s a lot easier to provide a scale and let the DM make up something appropriate than it is to provide a menu of options wirth the required numbers. (I do think numbers should be knowable by the PCs even in a scaled DC systems. Otherwise, you can’t reason about the approaches available to you, and it makes resolution less immediate, and that contribute to the fun.)
Firstly, I think it's incorrect to evaluate obstacles in terms of their difficulty in the way you're proposing here, and judging from the bolded bit, I think you largely agree. Obstacles should not scale in magnitude, but in kind to match increased player capability as levels increase. With a broad enough RNG, it's reasonable to have several grade of "gate" but that does not mean the conceit of "a locked portcullis in a sturdy wall" should produce a DC that's uncertain at all levels of play. It's fine and appropriate that there is a point that task falls off the RNG, and Take 10/20 help here, by making that a transition through 3 states. Initially it can be achieved at maximum effort given uninterrupted time (Take 20), then it can be achieved when not under immediate stress or perhaps by a character with a specialist feature, and finally it is not longer a challenge. Rolling becomes a risk you take when you have to, either because you're pushing the boundaries of what you can do, or because a situation is out of your control.
My assumption is the DM will be picking obstacles the same way they do monsters, which is by evaluating what’s available at the intended level of difficulty. The party is Xth level, which requires a set of CR Yth level monsters for some particular amount of challenge, and I want those to be undead, so I can pick from Z options. For that same Xth level party, if the DM wanted to include a trap or barrier, then the DM is going to look at things of the intended difficulty and pick from that list. In a sense, these things are helping to reinforce the game’s intended milieu by ensuring the challenges match what the characters are capable of doing.
As you intuit, I’m not a fan of the progression treadmill. I prefer the approaches used in old-school games and static DCs like PbtA games. As you get better, you get
better. If done well, your journey in competence goes from requiring a lot of help (and risk of consequences) to being self-sufficient (or nearly close to it). That’s how it worked in our Blades in the Dark game. In the beginning, we had to work together, push ourselves, and take devils’ bargains. By the end, we were doing solo scores and taking on big things by ourselves. I like that much better as a form of progression than what amounts to doing the same thing at higher levels but described more fantastically.
Secondly, many skill DCs should be attached to player facing abilities, not to obstacles in the world at large. If a player is provided the ability to "climb any sheer surface at half speed" by a DC X check, then the decision making is entirely out of the DM's hands. More abilities granted through the skill system should be declarative; that's exactly what spells do.
Non-combat specialities are a WIP in my homebrew system, but that’s how things work thanks to static DCs. If you want to make a map of an area you explored (thus allowing you to find it again without having to navigate back), you make a Skill Check using Cartography + Wisdom. If you want to cast from a scroll, that’s Scroll Use + Intellect. Spells work the same way as skills, but they use your Mage rank the method instead of a skill. That avoids the problem of spells being categorically better than skills. You’ll still want to invest in skills because there are trade-offs to using spells. They cost MP, which you can only recover normally with MP potions (that cost stress to consume) or by using a weekly downtime activity; and your Mage rank is derived from your level, but skills are bought with EXP and have a maximum rank of +5 that’s independent of level.
Once we stop conceiving as a DC 25 roll as "hard" and instead as "the requirement to use the 'open magical locks' power" the skill system moves away from a loop of the DM picking a difficulty and players tugging at the slots to see if they win the action they want. Designing a hard challenge means not picking numbers that players will achieve approximately 60% of the time, and instead in devising a situation that will require a novel use of their abilities (ideally iterated over time) to overcome.
I like this approach. It’s similar to the argument that old-school skills were actually providing you with something more than the baseline. A thief who uses Move Silently is not just sneaking about but is in actuality completely silent upon success. I don’t now how common that view was though at the time, and I think the idea of using that approach in a modern D&D-like might be a tough sell for some. (See also: the complaints people have about skill feats in PF2.)